Question

Find the equation of a curve passing through origin and satisfying the differential equation (1 + x²) dy/dx + 2xy = 4x².

Answer 1

Given: (1 + x²) dy/dx + 2sy = 4x² and (0,0) is a solution to the curve

To find: equation of curve satisfying this differential equation

Re-writing the equation as

Assume 1+x²=t

2x dx=dt

IF=1+x²

Therefore, the solution of the differential equation is given by

Satisfying (0,0) in the curve equation to find c

0=0+c

c=0

therefore, the equation of curve is